Problem: $\dfrac{ -q - 6r }{ 5 } = \dfrac{ -10q + 9s }{ -5 }$ Solve for $q$.
Explanation: Notice that the left- and right- denominators are opposite $\dfrac{ -q - 6r }{ {5} } = \dfrac{ -10q + 9s }{ -{5} }$ So we can multiply both sides by $5$ ${5} \cdot \dfrac{ -q - 6r }{ {5} } = {5} \cdot \dfrac{ -10q + 9s }{ -{5} }$ $-q - 6r = - \cdot \left( -10q + 9s \right) $ Distribute the negative sign on the right side. $-q - 6r = 10q - 9s$ $-{1}q - {6}r = {10}q - {9}s$ Combine $q$ terms on the left. $-{q} - 6r = {10q} - 9s$ $-{11q} - 6r = -9s$ Move the $r$ term to the right. $-11q - {6r} = -9s$ $-11q = -9s + {6r}$ Isolate $q$ by dividing both sides by its coefficient. $-{11}q = -9s + 6r$ $q = \dfrac{ -9s + 6r }{ -{11} }$ Swap signs so the denominator isn't negative. $q = \dfrac{ {9}s - {6}r }{ {11} }$